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# A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs. 498.96. If the cost of white-washing is 2.00 per square metre, find thei) inside surface area of the dome,ii) volume of the air inside the dome.

i)Given :
Cost of white washing the dome from inside = Rs. 498.96
Also, Cost of white washing 1 $${m}^2$$ area = Rs. 2.00

Therefore, CSA of the inner side of dome
= Rs. $$\frac{498.96}{2} {m}^2$$
= $$249.48 {m}^2$$

ii) Let the inner radius of the hemispherical dome be r.

Now, CSA of inner side of dome = 249.48 $${m}^2$$

But, CSA = $$2{\pi}{r}^2$$
$$\Rightarrow$$ 249.48 $${m}^2$$ = $$2 × \frac{22}{7} × {r}^2$$
$$\Rightarrow$$ $${r}^2 = (\frac{249.48 × 7}{2 × 22})$$ $${m}^2$$
$$\Rightarrow$$ r = 6.3 m.

Also, we have,

Volume of air inside the dome = Volume of hemispherical dome
= $$\frac{2}{3}{\pi}{r}^3$$
= $$\frac{2}{3} × \frac{22}{7} × {6.3}^3$$ $${m}^3$$
= $$523.908$$ $${m}^3$$ (approx.)

Therefore, volume of the air inside the dome is $$523.908$$ $${m}^3$$.